We now discuss possible origins of the anomalous spatial propagation at room temperature. First, we note that the measured propagation velocity is orders of magnitude larger than typical values both for optical phonons, which are commonly characterized by rather flat energy dispersions, and acoustic phonons, whose velocity is typically below 10\(^3\)  m/s [numbers[1]}]. This suggests that the propagating signal does not have a purely phononic origin. Another potential explanation of the observed behavior is the excitation of rapidly propagating bulk or surface phonon-polaritons [numbers[2]}, [3]}]. However, as a result of the crystal inversion symmetry, the bulk phonon modes are Raman and not IR active, and therefore cannot participate in the formation of phonon-polariton modes. In addition, for this type of excitation we would expect to measure higher propagation velocities (\(>\) 5\(\times 10^6\)  m/s) due to the light-like nature of these modes (see Supplementary Materials Section S8). Finally, the disappearance of the propagation above T\(_C\)  is unlikely to be explained by this scenario, as the observed phonon modes characterize both the low and the high temperature phase of this material, which several recent works suggest being an insulator even above T\(_C\)  [numbers[4]}, [5]}]. We next consider the possibility of the propagation of quasiparticles (QPs) emanating from the excitation spot with velocity \(v_k=(\partial \epsilon _k/\partial k)\)  of the order of 10\(^5\)  m/s, which can excite phonons in their wake. However, at room temperature, the carrier relaxation time of QPs is usually only of the order of a few tens of femtoseconds, corresponding to a mean free path of a few nanometers [numbers[6]}, [7]}]. In addition, the emission of phonons by the QPs would generate oscillations that are not in phase as we average rings around the photoexcited region. In our experiments coherent behavior is observed on a much wider spatial range and on timescales extending to a few picoseconds. We contend that more coherent electronic oscillations (such as the case of plasmons) are unlikely to be excited in this experiment as the material is an insulator at equilibrium. Even after photoexcitation we therefore do not expect the probed region to host the required carrier population to support these modes.
An exciton-polariton, formed by uncondensed excitons at the conduction-band edge, is a final potential candidate that could explain the observed behavior without requiring the existence of any exotic ground state in the system. Yet, long-range and long-lived (several picosecond) excitations such as the ones that we detect require significant coupling between the light and matter modes and significant confinement. Considering that for comparable van der Waals materials the estimated Q factors for a 60 nm flake are \(\le \) 5 [numbers[3]}], we would not expect to observe modes with lifetimes longer than \(\sim \) 10 fs in our system (see Supplementary Materials Section S8). Very strong light-matter coupling (resulting in a Rabi splitting of the excitonic line larger than 100 meV) also would be required to achieve experimentally relevant velocities, yet no hints of this are observed in equilibrium measurements [numbers[9]}]. Finally, we are unaware of a mechanism by which these modes could be coherently excited with our pumping scheme, where the injection of quasiparticles with energies much larger than the bandgap will relax to the bandedge through successive stochastic relaxation processes. We therefore believe that these considerations make the exciton-polariton scenario rather remote, but analogous measurements in the mid-IR would be useful to more conclusively address this scenario.
